okay so the equation is -4.9t^2 - 39.2t + 1.6
If the rockets explode at the highest point (which max height is 80 meters) One of the rockets is schedules to explode 2 minutes and 28 seconds into the program. When should the rocket be fired from the barge? (How long, from start of the program, before the rocket is fired)
plllllleaaassse hellp! thanks so much and godbless
4 minutes ago - 4 days left to answer.
Additional Details
so t is height of an object
and this equation = H(t)
31 seconds ago
H(t) = -4.9t^2 - 39.2t + 1.6 ?
this is just a parabola, with vertex at t = 39.2/-9.8
Now that's a negative number. In fact, the equation indicates that the rocket was fired from 1.6m height, downward. Now, I think it was probably fired upward, so the equation should be
-4.9t^2 + 39.2t + 1.6
At t = -39.2/9.8 = 4 the rocket reaches maximum height of 80 m.
So, since it takes 4 seconds to reach max height, fire it 2'24" into the program.
To solve this problem, we need to find the time when the rocket reaches its maximum height of 80 meters. We also need to determine the time it takes for the rocket to reach that point from the start of the program.
Given the equation H(t) = -4.9t^2 -39.2t + 1.6, where H(t) represents the height of the rocket at time t, and t represents time in seconds, we need to find the value of t that corresponds to a height of 80 meters.
To do this, we can set H(t) equal to 80 and solve for t:
-4.9t^2 - 39.2t + 1.6 = 80
Simplifying the equation, we get:
-4.9t^2 - 39.2t - 78.4 = 0
Since this is a quadratic equation, we can solve for t using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -4.9, b = -39.2, and c = -78.4. Substituting these values into the quadratic formula, we get:
t = (-(-39.2) ± √((-39.2)^2 - 4(-4.9)(-78.4))) / (2(-4.9))
Simplifying further:
t = (39.2 ± √(1536.64 - 1526.24)) / (-9.8)
t = (39.2 ± √10.4) / (-9.8)
Now we have two possible values for t, which correspond to the times when the rocket reaches its maximum height. By taking the positive value:
t = (39.2 + √10.4) / (-9.8)
Calculating this expression, we get:
t ≈ -1.02 seconds
Since time cannot be negative in this context, we disregard this solution. Therefore, the positive value from the quadratic formula does not have any physical meaning in this scenario.
However, we need to find the time it takes for the rocket to reach its maximum height from the start of the program. To do this, we need to subtract the time when the rocket reaches its maximum height from the time the rocket is scheduled to explode (2 minutes and 28 seconds).
To convert 2 minutes and 28 seconds into seconds, we have:
2 minutes = 2 * 60 = 120 seconds
28 seconds = 28 seconds
So, the time scheduled for the rocket to explode is 148 seconds (120 + 28).
Now, subtracting the negative value we obtained earlier (t ≈ -1.02) from the scheduled explosion time:
148 - (-1.02) ≈ 149.02 seconds
Therefore, the rocket should be fired from the barge approximately 149.02 seconds (or 2 minutes and 29.02 seconds) before the rocket is scheduled to explode.